Question

Atiyah-Macdonald before proposition 4.9

score 92 · Answer 1 · 2024-01-28 17:34:31

92

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Atiyah-Macdonald before proposition 4.9

Published on 28 Jan 2024 - 17:34

score 107 · Answer 2 · 2026-04-03 23:02:10

107

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Find the generator of a cyclic group $(\ ^{\mathbb{Z}_{5}[x]}\!/\!_{(g(x))})^{*}$

Published on 03 Apr 2026 - 23:02

score 97 · Answer 3 · 2024-01-30 08:37:18

97

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prove that $char(R/I_n)$ divides $n$ for a ring $R$ and $I_n$ as an ideal

Published on 30 Jan 2024 - 8:37

score 48 · Answer 4 · 2026-04-09 04:34:07

48

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Does there exist an "arithmetically-defined" group embedded as some subset of all cosets $a\Bbb{Z} + b$? Because we easily have monoids...

Published on 09 Apr 2026 - 4:34

score 113 · Answer 5 · 2026-04-01 16:24:22

113

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In a commutative unity ring $R$, if $M$ is a maximal ideal then ring $R/M^n$ has only one prime ideal

Published on 01 Apr 2026 - 16:24

score 92 · Answer 6 · 2026-04-01 12:07:04

92

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Form of ideal generated by subset of noncommutative nonunital ring

Published on 01 Apr 2026 - 12:07

score 72 · Answer 7 · 2026-03-27 06:05:01

72

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Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Published on 27 Mar 2026 - 6:05

score 90 · Answer 8 · 2024-02-04 11:55:36

90

Views

Proving that an ideal is not principal on $\Bbb{R}[x,y]$

Published on 04 Feb 2024 - 11:55

score 123 · Answer 9 · 2026-03-25 22:05:57

123

Views

Counterexample of Divisibility of Ideals with Product of Ideals

Published on 25 Mar 2026 - 22:05

score 189 · Answer 10 · 2024-02-05 11:56:47

189

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If the quotient of an ideal is principal, is the original ideal principal?

Published on 05 Feb 2024 - 11:56

score 55 · Answer 11 · 2026-03-27 04:38:25

55

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Quotient module $\mathscr{O}[[X]] / \langle X^t , \pi^r \rangle $ is of finite-length

Published on 27 Mar 2026 - 4:38

score 74 · Answer 12 · 2026-03-26 17:42:30

74

Views

I'm confused by the last step when showing that $\Phi$ is well defined in the proof of 2nd isomorphism theorem for rings?

Published on 26 Mar 2026 - 17:42

score 36 · Answer 13 · 2026-04-01 18:14:31

36

Views

Fault in the proof that radical prime implies ideal is primary.

Published on 01 Apr 2026 - 18:14

score 65 · Answer 14 · 2024-02-10 20:09:30

65

Views

Homomorphism between direct product of two rings and a domain

Published on 10 Feb 2024 - 20:09

score 42 · Answer 15 · 2024-02-13 10:11:06

42

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Extended and Contracted Ideals in Ring of Fractions

Published on 13 Feb 2024 - 10:11

List Question

Atiyah-Macdonald before proposition 4.9

Find the generator of a cyclic group $(\ ^{\mathbb{Z}_{5}[x]}\!/\!_{(g(x))})^{*}$

prove that $char(R/I_n)$ divides $n$ for a ring $R$ and $I_n$ as an ideal

Does there exist an "arithmetically-defined" group embedded as some subset of all cosets $a\Bbb{Z} + b$? Because we easily have monoids...

In a commutative unity ring $R$, if $M$ is a maximal ideal then ring $R/M^n$ has only one prime ideal

Form of ideal generated by subset of noncommutative nonunital ring

Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Proving that an ideal is not principal on $\Bbb{R}[x,y]$

Counterexample of Divisibility of Ideals with Product of Ideals

If the quotient of an ideal is principal, is the original ideal principal?

Quotient module $\mathscr{O}[[X]] / \langle X^t , \pi^r \rangle $ is of finite-length

I'm confused by the last step when showing that $\Phi$ is well defined in the proof of 2nd isomorphism theorem for rings?

Fault in the proof that radical prime implies ideal is primary.

Homomorphism between direct product of two rings and a domain

Extended and Contracted Ideals in Ring of Fractions

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